In this paper, we propose a new kind of fractal kinetic hologram using fractal hypercomplex model for security purposes. The proposed fractal kinetic holograms consist of a sequence of computer-generated fractal images between which there are self-similarity. And on that basis, we can make 'fractal animated holograms.' The results indicate that the model is quite efficient for synthesis of fractal kinetic images. The generated fractal kinetic holograms can be used in the laser anti-counterfeiting field.